Only dead mathematics can be taught where the attitude of competition prevails: living mathematics must always be a communal possession.

The stimulus of competition, when applied at an early age to real thought processes, is injurious both to nerve-power and to scientific insight.

Only dead mathematics can be taught where the attitude of competition prevails: living mathematics must always be a communal possession.

Mathematics had never had more than a secondary interest for him ; and even logic he cared for chiefly as a means of clearing the ground of doctrines imagined to be proved, by showing that the evidence on which they were supposed to rest had no tendency to prove them. But he had been endeavouring to give a more active and positive help than this to the cause of what he deemed pure religion.